Least Common Multiple (LCM) of 189 and 136
The least common multiple (LCM) of 189 and 136 is 25704.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 189 and 136?
First, calculate the GCD of 189 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 136 = 1 remainder 53 |
| 2 | 136 ÷ 53 = 2 remainder 30 |
| 3 | 53 ÷ 30 = 1 remainder 23 |
| 4 | 30 ÷ 23 = 1 remainder 7 |
| 5 | 23 ÷ 7 = 3 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 27 | 3618 |
| 63 and 116 | 7308 |
| 107 and 119 | 12733 |
| 175 and 49 | 1225 |
| 50 and 32 | 800 |